Knots bounding minimal discs in $B^4$ are ribbon (Hass)

Write $S^3=\{x\in\mathbb R^4:\|x\|=1\}$, $B^4=\{x\in\mathbb R^4:\|x\|\le1\}$ and $D^2=\{z\in\mathbb R^2:\|z\|\le1\}$. A knot is the image $K=\gamma(\mathbb R)$ of a $C^\infty$, $1$-periodic map $\gamma:\mathbb R\to S^3$ that is injective on $[0,1)$ and has nowhere-vanishing velocity. Suppose $K$ bounds a slice disc $F:D^2\to B^4$ (smoothly embedded, transverse to $S^3$ along its boundary $K$) which is a minimal surface for the Euclidean metric of $\mathbb R^4$, i.e. its mean curvature vector vanishes at every interior point. Then

Thus a potential counterexample to the slice–ribbon conjecture cannot bound a minimal slice disc.

Formalization Note Minimality is IsMinimalOnDisk F: with first fundamental form $E,G',G$, the vector $G\,\partial_0\partial_0F-2G'\,\partial_0\partial_1F+E\,\partial_1\partial_1F$ lies in the image of $dF_z$ for all $\|z\|<1$.